Miniaturized Two-Pressure Generator for Relative Humidity

Transcription

1 Miniaturized To-Pressure Generator for Relative Humidity by Dr. Helmut Mitter The original publication is available at.springerlin.com DOI.7/s y ABSTRACT The concept and design of a miniaturized to-pressure humidity generator are presented. The generator is suitable for achieving relative humidity ranging from % to 95% ith uncertainties of under % at ambient temperature and can be used for the calibration of relative humidity instruments in the laboratory and on site. By virtue of the concept, the relative humidity achieved is traced to only pressure measurements. Further references are not necessary. A special adjustment algorithm enables standard industrial pressure sensors to be used. The to pressure sensors are synchronized by performing alignment at ambient pressure. The resulting correlation of the uncertainties leads to very small systematic errors in the humidity display. Each humidity generator can still be individually adjusted through comparison ith a chilled mirror hygrometer, the total uncertainty of the generator being largely determined by the uncertainty of this hygrometer. Any drift of the pressure sensors that occurs can be compensated for at any time by performing an alignment at ambient pressure ithout changing the individual adjustment of the generator. It can be demonstrated that the uncertainty of the displayed humidity remains practically unchanged over the course of a year by virtue of this alignment process. KEY WORDS humidity generator, miniaturized, relative humidity, traceable, to pressure generator

2 . INTRODUCTION With the maret for humidity meters for industrial and semi-industrial applications expanding rapidly, it is becoming increasingly useful to have calibration equipment that enables the measurand relative humidity to be traceable to international units. measuring chamber ith ducts for samples rel. humidity indication temperature indication samples indication selector sitch for devices under test rel. humidity adjustment (pressure regulator) Fig.. Miniaturized to-pressure generator HUMOR (E+E Eletroni, Austria). poer supply devices under test 4 VDC Various commercially available humidity generators are in principle suitable for providing this type of proof. Hoever, such systems are generally very complex and expensive and only suitable for stationary operation, rendering them unsuited to in-house quality control departments catering to a broad maret. Saturated, and also unsaturated, salt solutions are also still used for relative humidity calibration. In this case, hoever, it is very difficult, if not impossible, to demonstrate complete traceability to international units. Various miniaturized humidity generators are no also available on the maret. In most cases, these or on the principle of a mixed-gas generator ith an internal reference, ith either a dedicated chilled mirror hygrometer or a capacitive polymer sensor serving as the internal reference. In the first case, high system costs must be reconed ith. The second case provides a reference that to all intents and purposes exhibits the same stability and measuring uncertainty as most of the devices to be tested. A transportable, user-friendly humidity generator (Fig. ) employing the same oring principle as a to-pressure generator ill be presented. Basically, this device displays humidity using a fundamental technique analogous to, for instance, the reference humidity generator of NIST []. The traceability of the device is ensured by periodic calibration against a traceable chilled-mirror hygrometer. Beteen the periodic calibrations, the device operates ith high stability due to its fundamental basis. The generator ors at ambient temperature and therefore displays the relative humidity at a slightly elevated ambient temperature. The only operating resources required are a poer supply and compressed, oil-free air at. MPa. The aim of the paper is not to give a full uncertainty calculation of the generator but to demonstrate ho to minimize the influence of pressure sensor tolerance and drift on the performance of the generator by means of different adjustment procedures. v. / Modification rights reserved

3 . GENERATOR CONCEPT AND SETUP Compressed oil-free air is completely saturated ith ater vapour in a saturation chamber at a certain pressure depending on the requested relative humidity and fed to a pressure reduction unit via a heated line. The pressure of the gas is first regulated to 5 Pa above ambient pressure and then throttled to ambient pressure p a via a heated needle valve. The needle valve is used to set a gas flo of 3 l min -. This is largely independent of the pressure in the saturation chamber ([6], [7]), as the admission pressure of the needle valve is alays held stable at p a + 5 Pa. Finally, the humid gas is fed into a measuring chamber here the required relative humidity is achieved (Fig. ), and ultimately released into the open air via an exhaust line. By varying the pressure in the saturation chamber beteen approximately MPa and 5 Pa at an ambient pressure of p a = Pa, the relative humidity in the measuring chamber can be varied beteen % and 95%. The displayed relative humidity U in the measuring chamber is derived from the saturation vapour pressure in the saturator e (t,p ) [4] at temperature t and pressure p, the relationship beteen the pressures in the saturator and the measuring chamber, and the associated saturation vapour pressure in the measuring chamber at temperature t according to Eq. () and Eq. (). device under test measuring chamber saturation chamber (saturator) heated high-pressure line heated pressure regulator and needle valve for flo adjustment p measurement pressure supply (. MPa) ith pressure regulator (rel. humidity adjustment) p measurement lo-pressure line ith temp. conditioning Fig.. Principle scheme of the miniaturized to-pressure generator. v. / Modification rights reserved

4 U e ( t, p) p = e ( t, p ) p () e ( t, p) = e ( t) f ( t, p) () e (t) saturation vapour pressure in the pure phase in respect to ater [], [3] ƒ (t,p) enhancement factor of air [5] e (t,p) saturated vapour pressure of the actual system in the presence of air or nitrogen in respect to ater [4] The measuring chamber and saturation chamber are manufactured jointly from a solid, highly heat-conductive metal bloc (special Aluminium alloy), the measuring chamber being positioned in the saturation chamber (Fig. ). The generator has to be operated either ith distilled ater or deionised ater and the user is obliged to change the ater each month for purity reasons. Hoever, failing to change the ater for several months resulted in no measurable contamination effects on the achieved relative humidity. Before being discharged into the measuring chamber, the humid gas is also fed repeatedly through gas conduits inside the all of the saturator hich very effectively brings the temperature of the gas into equilibrium ith that of the saturator. These design features ensure that the saturator temperature t and measuring chamber temperature t are practically the same and Eqs. () and () can therefore be simplified: t = t = t U e ( t, p) p e( t) f ( t, p) p p f ( t, p) = = = e ( t, p ) p e ( t) f ( t, p ) p p f ( t, p ) (3a) Equality of temperatures is ensured by the construction of the chambers as described in Section and shon in Fig.. Also, the effects of changing environmental temperatures are shon in Fig. 7. Even if the ambient temperature differs by more then K from the chamber temperature, the effect on the achieved relative humidity is very small. Nevertheless, the user has to operate the generator under normal laboratory conditions ithout heat radiation sources. As the generator is operated in a restricted temperature range for an average temperature t, the relation ƒ(t,p )/ ƒ(t,p ) can be sufficiently approximated by a polynomial in p /p, ƒ(p /p ) f ( t, p) f ( t, p ) p f p (polynomial in p /p ) (3b) and the fundamental equation of a to-pressure humidity generator is obtained. U = p p p f p [%] (3) Apart from a small correction parameter that taes into account the real saturation behaviour of air, the displayed v. / Modification rights reserved

5 humidity depends only on the pressure relationship beteen the measuring chamber and the saturation chamber. The pressure measurement and its measuring uncertainty are therefore crucially significant. Although other device-specific properties such as temperature homogeneity and saturation behaviour play a role in calibrating a generator and can lead to either systematic display errors or increased uncertainty, this design means these properties ill not change significantly beteen the individual devices or over the course of time and can be corrected by adjusting the device. 3. ADJUSTMENT AND CALIBRATION CONCEPT A ey objective in the development of the humidity generator as to eep system costs lo. For the pressure measurement, industrial pressure transmitters ith a specified accuracy of.5 % of the maximum readout are used. A simple estimate shos immediately that the pressure sensor specification leads to an uncertainty of up to 6 % rh for the displayed relative humidity. In principle, this deviation could be corrected by adjusting the generator, e.g. ith reference to a chilled-mirror hygrometer. Hoever, similar problems are immediately encountered hen looing at the long-term stability of the pressure sensors, hich means that this procedure does not produce an acceptable result ithout employing additional measures. An adjustment concept is therefore implemented, in hich the tolerances and drifts of the sensors are largely cancelled out by means of softare-based adjustment of the to pressure sensors for p and p at ambient pressure, thereby ensuring the humidity generator achieves a high degree of accuracy and stability. The individual steps in the adjustment concept - basic adjustment - adjustment - alignment are presented in the sections that follo and an uncertainty estimate is performed for the humidity generator, both in its ne state and after one year. All steps of the adjustment concept can be repeated at any time, but usually for the user there is only the need to do step 3 (alignment). 3.. Basic adjustment For pressure measurement, industrial sensors ith a specified tolerance of.5 % of the measuring range are used, the specification being interpreted as a rectangularly distributed uncertainty. The pressure sensors are described by the folloing model: Saturation chamber p : Measuring range MPa p = a + a p (4) a = u(a ) = 5.8 Pa a = u(a ) = 5.8E-3 (=) (=) v. / Modification rights reserved

6 Measuring chamber p : Measuring range. MPa p = b + p (5) b = u(b ) =.5 Pa (=) p = p a p a...ambient pressure p, p measured values in saturation chamber and measuring chamber, respectively The uncertainties of the pressure measurement are derived from the models of the pressure sensors, Eqs. (4) and (5), using: / u( p ) = u ( a ) + p u ( a (6) [ ] ) u ( p) = u( b ) (7) As the aim of the paper is to point out the effects of pressure sensor tolerance and drift and ho to eliminate them by a special adjustment procedure, here the measurement uncertainties of p and p are neglected. Besides, the contribution of the measurement uncertainties of p and p is very small compared ith the effects of pressure sensor tolerance (~. %rh compared ith 6 %rh) If the pressure sensors are used ithout any additional measures, the uncertainty of the displayed relative humidity can be determined as follos from Eq. (3):.8 uncertainty contribution pressure sensors delta u, % rh measurement uncertainty using a chilled mirror hygrometer (=) rel.humidity u, % rh Fig. 3. Deviation of indicated relative humidity of 3 generators from a certified chilled-mirror hygrometer after basic adjustment. Uncertainty contributions of pressure sensors after basic adjustment, including the contribution of pressure measurement uncertainty and the measurement uncertainty using a chilled-mirror hygrometer of about. % at 5 % and.6 % at 75 %, respectively (all =), are also indicated v. / Modification rights reserved

7 u( U hich leads to the uncertainty mentioned above of ~ 6 % rh at 95 %rh (=) (the small correction made by the enhancement factors has been omitted here as it does not mae any significant contribution to the total uncertainty). In the basic adjustment, the generator is depressurized, both pressure sensors are read at ambient pressure pa, and the difference (p a ) = p (p a ) p (p a ) calculated. Using the difference, a corrected value p is calculated for the saturator pressure and a revised model equation is obtained for the corrected pressure p / p ) = u( p) + ( ) u p p p (8) p = a + a p p ) + ( pa) = b + a ( p a p a (9) and the uncertainty of p is u ( p ) = u ( b ) + ( p pa) u ( a) () Basically, the offset of the pressure measurement p at ambient pressure p a is corrected to the same value as p and the to pressure measurements synchronized at ambient pressure. The readings from the to pressure sensors thereby become correlated, ith total correlation at ambient pressure. The uncertainty of the displayed humidity, taing into account the correlation, is derived as follos from Eqs. (3), (5) and (9): [( p p ) u ( a )] p p p u ( U ) = u ( b ) a p p p p () It can easily be demonstrated that the uncertainty of the displayed relative humidity u(u ) for p = p = p a ( U = %) becomes exactly zero (total correlation). In practice, the uncertainty of the pressure measurements includes the standard deviation from random variations, the limited resolution of the electronics, and the sensor stability must also be taen into account, hich results in a further small residual uncertainty of approximately. % rh at the adjustment point. Figure 3 shos measurements of the displayed humidity compared to a certified chilled-mirror hygrometer after the basic adjustment. The uncertainty calculated as per Eq. () resulting from the pressure sensor tolerance is also shon, including the contribution from the pressure measurement uncertainty of about. %. Most measuring values lie ithin the uncertainty estimate of Eq. (). Hoever, if the measuring uncertainty of the chilled mirror hygrometer is also tae into account, all measurements and the uncertainty estimate resulting from the pressure sensor contribution are compatible after the basic adjustment. 3.. Adjustment of the humidity generator After the basic adjustment, the humidity generator is checed against a certified chilled-mirror hygrometer and the deviations are stored as a correction table. Figure 4 shos the setup for the calibration of the generator. The output of the gas stream into the measuring chamber is closed and the gas stream is discharged via a special insulated pipe. A Pt reference thermometer is placed ithin the pipe. The gas stream is then routed via a heated line and split by a T-section, ith one part (typically.5 l min - ) being sent to the chilled mirror hygrometer hile the rest is released into the open air via a needle valve controlling the gas stream split. Located behind v. / Modification rights reserved

8 needle valve flo meter chilled-mirror hygrometer (DPH) heated exhaust line Pt closed standard exhaust Fig. 4. Setup for verifying a generator (principle scheme) using a chilled-mirror hygrometer. the chilled-mirror hygrometer is a flometer to control the gas stream through the chilled-mirror hygrometer (DPH). When calculating the relative humidity from temperature and de-point temperature, the folloing ey uncertainty contributions are taen into account: DPH calibration uncertainty Stability of DPH in the calibration interval De-point stability during the measurement Pressure loss in the measuring line Pt calibration uncertainty Pt self heating Pt heat conduction Stability of the Pt in the calibration interval Temperature stability during calibration Spatial temperature inhomogeneity in the saturation and measurement chambers Resolution of the humidity generator When adjusted in this ay, the generator exhibits deviations from the chilled-mirror reference ithin the specified tolerance indicated in Fig. 5. The total uncertainty of the generator is calculated from the specification limits (rectangular distribution) and the uncertainty of the calibration using the chilled-mirror hygrometer. The spatial v. / Modification rights reserved

9 u(u ), % ( = ) total uncertainty HUMOR accuracy (specification) uncertainty of reference measurement rel.humidity u, % Fig. 5. Specification, calibration uncertainty, and total uncertainty (=) of a ne generator. distribution of the relative humidity ithin the measuring chamber is largely determined by the temperature inhomogeneity of. C (difference beteen maximum and minimum values, rectangularly distributed) in the measuring chamber, varies from.3 to.33 % rh depending on the displayed humidity, and is included in the uncertainty calculation Alignment By means of the adjustment outlined in Section 3., all systematic deviations of the generator from an ideal generator ere corrected, ithin the measuring uncertainty of a DPH. In particular, the systematic readout errors of the pressure sensors ere also corrected. During operation, hoever, a generator drift must be reconed ith. This derives almost exclusively from drift of the pressure sensors. For the pressure sensors, the manufacturer specifies a maximum drift per year of.5 Pa (p ) or Pa (p ). For the annual drift, manufacturer s specifications (rectangular distributed) are doubled, resulting in the folloing models for the additional uncertainty of the pressure measurement after one year, based on Eqs. (4) and (5): p = a' + a'' p () a = u(a ) =.3 Pa (=) a = u(a ) =.3E-3 (=) p = b ' + p a (3) b = u(b ) =.5 Pa (=) Exactly as ith the basic adjustment in Section 3., here too the generator is depressurized and the pressure sensors are once again synchronized at ambient pressure. Unlie the basic adjustment, hoever, the generator correction values as per Section 3. v. / Modification rights reserved

10 u(u ), % ( = ) total uncertainty (ne) total uncertainty after year drift contribution pressure sensors change in total uncertainty after year rel.humidity u, % Fig. 6. Total uncertainty of a ne generator and after one year. Also, the drift contributions of the pressure sensors and the change in total uncertainty after one year are indicated (=). are retained in the alignment, i.e. only the change occurring ithin one year is examined. The additional uncertainty contribution after a year is then derived as follos, according to Eq. (): [( p p ) u ( a ')] p p p u ( U ) = u ( b ') a p p p p (4) Figure 6 shos the uncertainty contribution resulting from the drift after one year. An additional contribution resulting from the resolution of the electronics has also been taen into account. The total uncertainty hen ne and after one year, and the increase in uncertainty after one year, have also been entered. The generator can be aligned by the user at any time and as often as required. An alignment is particularly recommended henever the humidity readout deviates significantly i.e. more than.3 % rh from % rh hen the generator is depressurized. 4. MEASUREMENTS For stable humidity display, the generator requires only a room ith normal climatic conditions and no direct sources of thermal radiation. In order to demonstrate the stability of the humidity display ith fluctuating temperatures, a generator as stabilized at 75 % and exposed to changing temperature conditions in a temperature cabinet, hile at the same time the displayed humidity as monitored ith a chilled-mirror hygrometer (Fig. 7). At different ambient temperatures of C, 5 C, and 4 C, the largest change in the achieved humidity is less than. % rh. During the temperature change from C to 5 C and from 5 C to 4 C, the humidity display v. / Modification rights reserved

11 deviation of achieved rel.humidity delta.u, % time, min Fig. 7. Influence of the ambient temperature t a. Different ambient temperatures of C, 5 C, and 4 C lead to a change in achieved relative humidity of less than. %. ta = 5 C --> 4 C ta = C --> 5 C temperature difference measuring chamber to ambient temp., K deviation from adjusted value, % rh delta generator delta sample adjusted value adjusted rel.humidity u, % -. time, hour Fig. 8. Response of generated humidity and of a device under test after selecting a ne value. is incorrect by less than %, even though there is a difference of up to C beteen the temperature of the generator s measuring chamber and the ambient temperature. Figure 8 shos the response of the humidity display over time, the deviation of a humidity meter aaiting calibration from the displayed humidity, and the deviation of the generator from the target humidity. The target humidity is stable to ithin. % rh after a fe minutes; the setting time is primarily determined by the speed at hich a ne target pressure can be set in the saturator. The setting response of the device under test is largely determined by its properties. The generator itself maes practically no contribution to the stabilization time. The humidity generator can be traced to international units (SI units) by means of its calibration against a certified chilled-mirror hygrometer. Because of its high stability and small uncertainty, it is used as a humidity reference device in various calibration laboratories. v. / Modification rights reserved

12 . deviation from reference, % rh NMI t = 5 C NMI t = C HUMOR t = 4 C -. relative humidity u, % Fig. 9. Comparison of calibration measurements using - the described miniaturized to-pressure generator (HUMOR ) - the national Austrian reference generator (NMI) The uncertainties of each generator (=) are indicated. Figure 9 compares the calibration of a humidity meter based on a capacitive polymer sensor carried out using the Austrian national standard generator at temperatures ( and 5 C) ith a calibration using the described HUMOR miniaturized to-pressure generator as a reference device of the Austrian Calibration Service (ÖKD). The accredited uncertainties (=) are shon for each case. Within the combined measuring uncertainties, no differences in the calibrations can be identified. References. S. Hasegaa, J.W. Little, J. Res. Nat. Bur. Stand. 8A, 8 (977). A. Wexler, J. Res. Nat. Bur. Stand -A. Physics and Chemistry 8A, 775 (976) 3. D. Sonntag, Z. Meteorol. 7, 34 (99) 4. L.P. Harrison, in Humidity and Moisture, Vol. 3, Fundamentals and Standards, A.Wexler, W.A.Wildhac, (Eds.) (Reinhold Publishing, Ne Yor 965), pp L. Greenspan, J. Res. Nat. Bur. Stand -A. Physics and Chemistry 8A, 4 (976) 6. Accorded patent, US B 7. Accorded patent, EP B v. / Modification rights reserved